Turing Degrees of Limit Sets of Cellular Automata

Alex Borello,Pascal Vanier,Julien Cervelle

doi:10.1007/978-3-662-43951-7_7

Turing Degrees of Limit Sets of Cellular Automata

Alex Borello, Pascal Vanier + Show 1 more

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https://doi.org/10.1007/978-3-662-43951-7_7

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Publication Date: Jan 1, 2014

Citations: 2

Affiliation: University of Paris-Est, Université Paris Cité, Université Paris-Est Créteil

#Limit Sets Of Cellular Automata #Computable Point + Show 8 more

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Abstract

Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of limit sets of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point.

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